What is the integral of sin(x)e^{-cos(x)} ?

The integral of sin(x)e^{-cos(x)} is e^{-cos(x)}+C

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integral of sin(x)e^{-cos(x)}

\int sin (x) e^{- c o s (x)} d x

e^{- c o s (x)} + C

Solution steps

\int sin (x) e^{- c o s (x)} d x

Apply u-substitution

= \int e^{u} d u

Use the common integral:

\int e^{u} d u = e^{u}

= e^{u}

Substitute back

u = - cos (x)

= e^{- c o s (x)}

Add a constant to the solution

= e^{- c o s (x)} + C

What is the integral of sin(x)e^{-cos(x)} ?
The integral of sin(x)e^{-cos(x)} is e^{-cos(x)}+C